In a recent paper [Salimov, A., Asl, M.B., Kazimova, S.: Problems of lifts in symplectic geometry. Chin Ann. Math. Ser. B. 40(3), (2019), 321-330] the authors have investigated the curious fact that the canonıcal symplectic structure dp = dpi ∧ dxi on cotangent bundle may be given by the introduction of symplectic isomorphism between tangent and cotangent bundles. Our analysis began with the observation that the complete lift of the symplectic structure from the base manifold to its tangent bundle is being a closed 2-form and consequently we proved that its image by the simplectic isomorphism is the natural 2-form dp. We apply this construction in the case where the basic manifold of bundles is a Riemannian manifold with metric g and consider a new 1-form ω = gijyjdxi and its exterior differential on the tangent bundle, from which the symplectic structure is derived.
Tangent bundle 2-form symplectic manifold complete lift musical isomorphism
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Araştırma Makalesi |
Yazarlar | |
Erken Görünüm Tarihi | 23 Temmuz 2022 |
Yayımlanma Tarihi | 31 Ekim 2022 |
Kabul Tarihi | 18 Temmuz 2022 |
Yayımlandığı Sayı | Yıl 2022 Cilt: 15 Sayı: 2 |